A plane directly above Denver, Colorado, (altitude 1650 meters) flies to Bismark, North Dakota (altitude 550 meters). It travels at 625 km/hour along a line at 8250 meters above the line joining Denver and Bismark. Bismark is about 850 km in the direction $60^{\circ}$ north of east from Denver. Find parametric equations describing the plane's motion. Assume the origin is at sea level beneath Denver, that the $x$-axis points east and the $y$-axis points north, and that the earth is flat. Measure distances in kilometers and time in hours.

$\vec r(t) =$